How to parent a cloth to a rigged mesh?
This doesn't answer your question exactly, but it might produce the result your looking for. 

First un-parent the banner. Then clear the location(Alt + G). Add a Curve modifier and add your path as the curve object with Y as the deform axis. If the rotation is now wrong, rotate on the Y axis 90 degrees. Make sure your at the first frame of the animation, and move the banner on the Y axis until it is positioned behind the bird. Set a location keyframe(I, then "Location"). Go to the end of the animation and move the banner on the Y axis until it is again positioned behind the bird(type 302 into Y location it will get you close). Set another location keyframe. Go to the Graph Editor and under Key->Interpolation Mode choose "Linear".

So its not using a cloth simulation, but it should do what you want.